Question Type 8: Solving questions with the values of inverses Exercises

Let $f(x)=\frac{1}{x}$ for $x\neq0$. Find the inverse function $f^{-1}(x)$ and then evaluate $f^{-1}(2)$.

Given $f(2)=5$, $f(3)=6$, $f(6)=8$, and $f\left(\frac{1}{6}\right)=18$, find $f^{-1}(6)$.

The temperature in Fahrenheit is given by: $F = f(C) = \frac{9}{5}C + 32.$ Find the inverse function $f^{-1}(F)$ and compute $f^{-1}(212)$.

The total cost in dollars of producing $x$ units is $C(x)=50+2x$.

Find an expression for $C^{-1}(y)$. Interpret what $C^{-1}(y)$ represents and find the value of $C^{-1}(150)$.

An invertible function $g$ satisfies $g(1)=2$, $g(2)=5$, and $g(5)=12$. Find $g^{-1}(12)$.

An account balance grows as $A(t)=100(1.05)^t$, where $t$ is the number of years. Find an expression for the inverse function $A^{-1}(A)$ and determine the value of $t$ when $A=200$.

If $f^{-1}(4)=9$ and $f^{-1}(7)=2$, determine $f(2)$ and $f(9)$.

For an invertible function $h$, given that $h(-1)=4$, $h(2)=-3$, and $h(-3)=2$, determine $h^{-1}(-3)$.

Given $f(2)=5$, $f(3)=6$, $f(6)=8$, and $f\left(\frac{1}{6}\right)=18$, find $f^{-1}(8)$.

Given $f(4)=10$, $f(7)=20$, and $f(10)=30$, find $f^{-1}(30)$.

An invertible function $f$ has $f(1)=3$, $f(3)=8$, and $f(8)=15$. Evaluate $f^{-1}(15)$ and then $f^{-1}\bigl(f^{-1}(15)\bigr)$.